Parallel normalized preconditioned conjugate gradient type methods based on normalized approximate finite element inverse matrix techniques are investigated for the efficient solution of sparse linear systems. Application of the proposed methods on a three dimensional boundary value problems is discussed and numerical results are given. The parallel implementation of the normalized precondition...

In this paper we present a new result on evaluating the difference between two dynamical systems. Extending the idea of information theoretic gap developed in [2], we first describe a symmetric version of information gap between dynamical systems. This metric has the advantage of being positive semi-definite and symmetric. A numerical method is developed to compute the symmetric Kullback-Leible...

In this Note we prove that in two and three space dimensions, the symmetric and non-symmetric discontinuous Galerkin method for second order elliptic problems is stable when using piecewise linear elements enriched with quadratic bubbles without any penalization of the interelement jumps. The method yields optimal convergence rates in both the broken energy norm and, in the symmetric case, the ...

We initiate a Stein’s method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov’s central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the proof gives an error term. The construction of an exchangeable pair needed for applying Stein’s method arises from the theory of harmonic function...

This paper is concerned with the numerical computation of cavitation in nonlinear elasticity. The Crouzeix-Raviart nonconforming finite element method is shown to prevent the degeneration of the mesh provoked by the conventional finite element approximation of this problem. Upon the addition of a suitable stabilizing term to the elastic energy, the method is used to solve cavitation problems in...

Several Krylov subspace iterative methods have been proposed for the approximation of the solution of general non-symmetric linear systems. Odir is such a method. Here we study the restarted version of Odir for non-symmetric inde nite linear systems and we prove convergence under certain conditions on the matrix of coe cients. These results hold for all the restarted Krylov methods equivalent t...

The symmetric rank-one update method is well-known in optimization for its applications in the quasi-Newton algorithm. In particular, Conn, Gould, and Toint proved in 1991 that the matrix sequence resulting from this method approximates the Hessian of the minimized function. Extending their idea, we prove that the symmetric rank-one update algorithm can be used to approximate any sequence of sy...